Question

Which of the following equation has no solution?

• A. $\sec \theta =23$
• B. $\cos \theta =\sqrt{2}$
• C. $\tan \theta =2019$
• D. $\sin \theta =-\frac{1}{5}$

Answer 1

The correct option is B $\cos \theta =\sqrt{2}$

We know that ,

1.$sin\theta$ and $cos\theta$ lie in between $[-1,1]$.

2. $tan\theta$ and $cot\theta$ lies in between $(-\infty ,+\infty )$

3. $cosec\theta$ and $sec\theta$ lies in between $(-\infty ,-1]\cup [1,\infty )$

Which shows that $A$,$C$,$D$ are true.

Now $\sqrt{2}=1.414$ > $1$.

Hence it has no solution as per the above mention condition